hw6-s10-430

hw6-s10-430 - K is required for a zero steady-state error?...

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ECE 382 Homework 6 Due: Thursday, Feb. 4, 2010 1) A unity feedback system has an open-loop transfer function: G ( s ) = 6 ( s + 4 ) s ( s 2 + 2 )( s + 3 ) a) Determine the static position error constant K p , the static velocity error constant K v , and the static acceleration error constant K a . b) Determine the steady-state error e ss = lim t e ( t ) where the input is r ( t ) = ( 2 t + 5 ) u ( t ) . 2) Repeat Problem 1 for a feedback control system whose G ( s ) and H ( s ) are respectively: G ( s ) = 3 s ( s + 3 ) ( s + 1 )( s 2 + 2 s + 4 ) H ( s ) = ( s + 1 )( s + 4 ) s 2 What is the type number of the system? 3) Given the following closed-loop system: R(s) C(s) 3.5 s(s 2 + 2s + 3.6) + _ Ks + 1 If we re-define the system error e ( t ) = r ( t ) - c ( t ) , and r ( t ) = 10 tu ( t ) , what value of
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Unformatted text preview: K is required for a zero steady-state error? 4) A unity feedback system has the forward transfer function G ( s ) = K ( s + 2 ) s ( s + 3 )( s + 1 ) 2 The input r ( t ) = 1 + 3 t is applied to the system. a) It is desired that the steady-state error be equal to or less than 0.1 for the given input function. Determine the minimum value that K must have to satisfy this requirement. b) By use of Rouths stability criterion, determine whether the system is stable for the minimum value of K determined in part a)....
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